Renormalisation-group analysis of electromagnetic couplings in the pionless effective field theory

TL;DR

This paper applies the Wilsonian renormalisation group to analyze electromagnetic interactions in pionless effective field theory, deriving a renormalisation group equation and exploring scaling behavior near the unitary limit.

Contribution

It introduces a renormalisation group framework for electromagnetic couplings in pionless EFT, linking gauge invariance, power counting, and short-range physics.

Findings

Derived a renormalisation group equation for the interaction current density.

Identified fixed points and scaling behavior near the unitary limit.

Connected scaling of current terms to observable form factors.

Abstract

The Wilsonian renormalisation group is applied to a system of two nonrelativistic particles interacting via short-range forces and coupled to an external EM field. By demanding that a fully off-shell one-particle-irreducible 5-point amplitude is independent of the cutoff, a renormalisation group equation is derived for the interaction current density. This is solved to obtain the fixed point corresponding to the unitary limit. The scaling behaviour of perturbations around this point is analysed. Some of these terms are related by gauge invariance to terms in the effective-range expansion; others describe short-range physics that is not included in the two-body potential. We construct observables including the bound-state form factor and show how the scaling of the terms in the interaction current is reflected in the power counting for their contributions to observables.